Richmond High math teacher Andrew Kim, 23, gives details about the new free, SAT math prep class held after school weekly - the students are Joey Lumagbas (left), Joey Saephan and Raul Vicuna III, all 17.

Photo: Leah Millis, The Chronicle

Richmond High math teacher Andrew Kim, 23, gives details about the...

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Joey Lumagbas works on a math problem during Richmond High's free class to prepare for the SAT college entrance test.

Photo: Leah Millis, The Chronicle

Joey Lumagbas works on a math problem during Richmond High's free...

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Jackie Ayala, 17 (left), helps out Miguel Bernal, 17, with a problem during the weekly SAT math prep class. More than 1,600 district seniors are signed up to take the exam, nearly 80 percent of the class of 2014.

Photo: Leah Millis, The Chronicle

Jackie Ayala, 17 (left), helps out Miguel Bernal, 17, with a...

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Teacher Andrew Kim discusses functions during an SAT math prep class held after school that Richmond High offers anyone who wants to attend.

The group of students in Andrew Kim's classroom stared at the handout full of math problems and focused on question 1.

"If the function f is defined by f(x) = 3x + 2, and if f(a) = 17, what is the value of a?

The Richmond High School teens, all 12th-graders, furrowed their brows as brief flashes of panic crossed their faces.

In less than a week, they would be taking the SAT, the high-stakes exam that likely will play a big role in determining whether they land at their college of choice or one of their Plan B safety schools.

But unlike teens across the country who typically pay $51 and then schlep to an unfamiliar location early on a designated Saturday morning to take the anxiety-inducing test, the seniors in Kim's after-school SAT tutoring session will take the exam Wednesday at their own school, during school - for free.

And that offer applies to every senior in the West Contra Costa Unified School District.

The East Bay district is the first in California to hold an official SAT School Day, giving every 12th-grader an easy opportunity to take the exam for free during the school day.

So far, more than 1,600 seniors across the district are signed up to take the exam, nearly 80 percent of the class of 2014.

West Contra Costa will join 60 districts nationwide and all schools in Delaware, Idaho and Washington, D.C., offering SAT School Day on Oct. 16.

The district will cover the cost of the exam for students who don't qualify for a waiver.

No reason not to take it

The College Board, which oversees the SAT and other college entrance exams, started sponsoring the annual event four years ago and provides access to an online SAT course as well as other study materials to students in participating districts who want to take the test.

The district has taken away every justification students use not to take it, said Finy Prak, a West Contra Costa district counselor on special assignment.

"You're not paying for it. All your friends are doing it. Your teachers are proctoring it," she said. "We've knocked down every excuse, every barrier, every wall they use as a reason for not taking it."

The district also pays for students to take the PSAT and Ready Step, which are for eighth- through 11th-grade students and help evaluate student skills before they take the SAT.

Vocabulary is key

At Richmond High, dozens of seniors this fall have been taking advantage of after-school SAT prep classes in English and math to get ready for the exam.

One of the biggest issues for students is the vocabulary used in reading passages as well as in questions, said Angelica Arriaga, a program director for the school-based nonprofit College is Real.

"That's the biggest disadvantage," she said. "If they don't understand the question they can't answer it."

With only a week until the test, Arriaga wasn't focusing on teaching vocabulary or other English skills.

She used the 888-page Official SAT Study Guide to help students become familiar with the format of the test, time management techniques and how to determine which questions to skip and which to come back to if there's time.

"This test is all about strategy," she said.

Back in Andrew Kim's classroom after school last week, the Richmond High math teacher was focusing on both content and strategy.

Functions will be on the test, he told the 10 students huddled toward the front of class.

You all learned functions in algebra or advanced algebra, he told the teens.

"What's challenging about the SAT is how they ask the questions," he said. "It's all about exposure to the SAT type of questions."

For an hour, he went through several f(x) types of questions, helping students understand what each question was asking.

Raul Vicuna debated with fellow students as they worked through the problems.

Answer to the question

The value of a in the first question, they decided, was answer A: 5.

Raul, 17, had already taken the SAT once, on an early Saturday morning in El Cerrito, but would take it again Wednesday at school to try to improve his score.

He loved the idea of an accessible exam at his own school when he had to be there anyway.

Even classmates not applying to four-year colleges were aware of the opportunity.

"More people in the school know about it," he said. "They know even if they don't want to take it."